Arching of Railway Turnouts by Analytical Design Method

The paper involved the issue of arching of the railway turnouts. This is an issue which is given relatively less attention to scientific and research activities. Reference has been made to the book by Wladyslaw Rzepka, under the title “Curved turnouts in plan and profile”, which has been used in Poland for more than 50 years as the main source of information relating to the turnouts on the curve. The book is a compilation of elaborations describing the contemporary state of knowledge being to a large extent a display of German achievements of the forties and fifties in the twentieth century. It has been pointed out that the theory accumulated in the book was adapted to the contemporary calculation needs. The major drawback in the given solutions seems to be ambiguity in the adopted reference system. In the present study an analytical approach is made to the subject matter, and the adopted system of coordinates is connected to the initial position of the turnout being arched. Three possible turnout arching variants have been analyzed to determine some universal mathematical relations. They describe the coordinates of the main track end and the diverging one, the value of the circular arc radius of the diverging track and equations of both the tracks. The analytical record also proves useful for authentic applications. It should be noted that it may be particularly beneficial to use the analytical method to design connections of parallel tracks located in a circular arc (using curved turnouts).